Question

select the correct answer.

a sphere has a radius of 6.2 centimeters. what is the approximate lateral surface area?

\\(77.9\text{ cm}^2\\)

\\(241.5\text{ cm}^2\\)

\\(483.1\text{ cm}^2\\)

\\(39.0\text{ cm}^2\\)

Explanation:

<pre_analysis>
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<reasoning>

State the surface area formula for a sphere

\[
S = 4\pi r^2
\]

Substitute the given radius and calculate

\[

$$\begin{aligned} r &= 6.2\text{ cm} \\ S &= 4 \times \pi \times (6.2)^2 \\ S &= 4 \times \pi \times 38.44 \\ S &= 153.76\pi \\ S &\approx 153.76 \times 3.14159265 \\ S &\approx 483.05\text{ cm}^2 \end{aligned}$$

\]

Match with the closest option

\[
S \approx 483.1\text{ cm}^2
\]
</reasoning>

<answer>
<mcq-option>(A) \(77.9\text{ cm}^2\)</mcq-option>
<mcq-option>(B) \(241.5\text{ cm}^2\)</mcq-option>
<mcq-correct>(C) \(483.1\text{ cm}^2\)</mcq-correct>
<mcq-option>(D) \(39.0\text{ cm}^2\)</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Geometry",
"Surface Area of Spheres"
]
}
</post_analysis>

Answer:

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"concepts_used": [],
"new_concepts": [
"Surface Area of Spheres"
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"Surface Area of Spheres"
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</pre_analysis>

<reasoning>

State the surface area formula for a sphere

\[
S = 4\pi r^2
\]

Substitute the given radius and calculate

\[

$$\begin{aligned} r &= 6.2\text{ cm} \\ S &= 4 \times \pi \times (6.2)^2 \\ S &= 4 \times \pi \times 38.44 \\ S &= 153.76\pi \\ S &\approx 153.76 \times 3.14159265 \\ S &\approx 483.05\text{ cm}^2 \end{aligned}$$

\]

Match with the closest option

\[
S \approx 483.1\text{ cm}^2
\]
</reasoning>

<answer>
<mcq-option>(A) \(77.9\text{ cm}^2\)</mcq-option>
<mcq-option>(B) \(241.5\text{ cm}^2\)</mcq-option>
<mcq-correct>(C) \(483.1\text{ cm}^2\)</mcq-correct>
<mcq-option>(D) \(39.0\text{ cm}^2\)</mcq-option>
</answer>

<post_analysis>
{
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"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Geometry",
"Surface Area of Spheres"
]
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